In this exercise we have to use knowledge of Taylor polynomials to calculate the equations given in the text.
A) [tex]F^4(0)=108[/tex]
B) [tex]R_N(x) \leq 0.012170471[/tex]
In this exercise we will use the given polynomials to calculate as follows:
A) We have:
[tex]f(x)= e^{3x^2}\\f(0)=1[/tex]
So when we derivate the equation we have that:
[tex]f'(x)= 6xe^{3x^2}\\f'(0)=0\\f''(x)= (6+36x^2)e^{3x^2}\\f''(0)=6\\f'''(x)= 108x(2x^2+1)e^{3x^2}\\f'''(0)=0\\f''''(x)= (1296x^4+1296x^2+108)e^{3x^2}\\f''''(0)= 108[/tex]
B) we have that:
[tex]T_3(x)= 1+3x^2\\R_N(x)= T_3(x)-f(x)\\R_N(x) \leq 0.012170471[/tex]
See more about Taylor polynomial at brainly.com/question/23842376
